1. Field of the Invention
The present invention relates to a method for calibrating the strapdown inertial navigation system of a taxiing aircraft. More particularly, this invention pertains to a method for improving the performance of an on-board calibration system that corrects gyro bias errors by observing indicated inertial velocities.
2. Description of the Prior Art
Aircraft inertial navigation relies upon the integration of data throughout a sequence that is begun when the aircraft is prepared for takeoff and which ends when the aircraft has landed and motion has ceased. The inertial navigation apparatus of an aircraft includes various components, including accelerometers and gyroscopes, that convert the effects of inertial forces into acceleration, velocity and position measurements. The accelerometers determine acceleration forces along three orthogonal sensitive axes and this data is converted, through integrations, into the aircraft's velocity and position. In a strapdown system in which the accelerometers are fixed in relation to the geometry of the aircraft, the gyroscopes that measure the aircraft's attitude also measure that of the accelerometer platforms. The data measured by the gyros is utilized to resolve the accelerometer outputs continuously along the appropriate space axes.
The standard inertial instruments are well-suited for obtaining the necessary flight data in an aircraft when airborne. However, important calibration processes take place at the beginning of the flight and prior to the airborne phase to assure that the ultimate measurements of acceleration, velocity and position are substantially free of inaccuracy and bias. Thus, during initial alignment, the precise location and the attitudes of the inertial navigation instruments must be determined and entered into the flight computer, a process that corresponds to the "leveling of the reference platform" that takes place in a non-strapdown or gimballed navigation system.
After initial instrument alignment, the flight computer enters the navigation mode and remains in this mode for the remainder of the flight. While in the navigation mode, the flight computer receives information from the accelerometers and keeps track of the attitudes of the inertial instruments by means of the gyros. Such attitude information is received from the integration of the rate signals received from the gyroscopes.
The initial alignment mode also serves as an opportunity to correct instrument errors. An important error of this sort is the body component of gyro bias error. This error refers to the fixed offset or bias of the angular rate output of the gyros along the aircraft's pitch and roll axes. Unfortunately, in the prior art it has only been possible to partially correct this error.
Conventionally, this problem is addressed by resolving the gyro rates about the pitch and roll axes to a north and east system. A process known as "mini biasing" is then employed during alignment (and prior to taxiing) to correct the gyro components along the northern axis. Unfortunately, the error components along the east axis are unobservable during initial alignment. Such unobservability follows from the fact that the initial azimuth determination (i.e. gyrocompassing) utilizes the east component of the gyro outputs to determine azimuth since it is known that the east component of the Earth's angular rate should be zero. Thus, such components are assumed to be correct. That is, the direction of the Earth's rotation rate is employed to determine the initial azimuth of the instrument platform.
FIGS. 1(a) and 1(b) are top plan views of an aircraft during the alignment mode and the taxiing portion of the navigation mode respectively. As shown in FIG. 1(a), at the end of alignment the east component of gyro bias error .epsilon..sub.E.sbsb.o is balanced by the west component of the Earth's angular rate error .delta..OMEGA..sub.W (=.phi..sub.z .times..OMEGA..sub.N where .OMEGA..sub.N is the north component of the earth's angular rotation rate) resulting from a residual azimuth error .phi..sub.z. For this reason, velocity errors are not observed until the aircraft changes heading during the taxiing portion of the navigation phase. As shown in FIG. 1(b), when a change of heading occurs, the original east gyro bias error .epsilon..sub.E.sbsb.o will rotate with the taxiing aircraft and will no longer lie in the east coordinate direction. The west component of the Earth's angular rate error .delta..OMEGA..sub.W will continue to lie in the west coordinate direction as it is determined by the navigation reference axes rather than by the aircraft body axes.
The absence of a method for determining or, needless to say, correcting the east axis component of gyro error .epsilon..sub.E.sbsb.o can lead to significant difficulties during flight as this error .epsilon..sub.E.sbsb.o will cause position errors to accumulate as a result of the integration process in aircraft navigation.
A method for overcoming the above-referenced inability to observe the east component of gyro bias error during the alignment phase is described by the inventor in "Calibration of a Ring Laser Gyro Inertial Navigation System For Minimum Velocity Error", Fourteenth Biennial Guidance Test Symposium, Central Inertial Guidance Test Facility, Guidance Test Division, 6585th Test Group, Holloman AFB, Vol. II (Oct. 3, 4, 5, 1989) at pages 1-1 through 1-20. That paper describes a system for inferring the original east component of gyro error .epsilon..sub.E.sbsb.o through observations made during the post-alignment taxiing portion (i.e. as shown in FIG. 1(b)) of the navigation phase. The method operates upon the known relationship between the cross-heading velocity of a taxiing aircraft and the original east component of gyro bias error.
As mentioned earlier, once an aircraft begins taxiing and changes heading, the east component of gyro bias error and the west component of the Earth rotation rate error are no longer balanced as the original east component of gyro bias error rotates with the body of the aircraft while the west component of the Earth rotation rate error remains aligned with the reference system. As a consequence, north and east velocity errors begin to build up and those errors form the basis for the determination of the east component of the gyro bias error. Although the north and east velocity errors cannot be observed directly, the cross-track component of velocity error, V.sub.CT, can be observed, and its relationship to the north and east velocity errors is known.
FIG. 2 is a top plan view of a taxiing aircraft for illustrating the above-described process for inertial instrument calibration in which the cross-track velocity V.sub.CT is employed as a surrogate for the north and east velocity errors. The method described in the above-identified paper relies upon the fact that the velocity in the cross-track direction (axis 2) should be zero as the cross-track direction is, by definition, perpendicular to the true velocity vector V.sub.G. Because of the presence of the north and east velocity errors, V.sub.CT normally has a finite value. However, the value of V.sub.CT is itself corrupted by the presence of a number of errors, discussed below.
The inertial system 4 does not know the exact cross-track direction. However, when taxiing, the cross-heading direction (axis 6) differs from cross-track direction only by a small crab angle .beta. as shown in FIG. 2. According to the above-identified paper, the cross-heading velocity V.sub.C is observed, and is then corrected by using an estimated crab angle .beta. to obtain estimated cross-track velocity V.sub.CT. An additional correction is made for lever arm R.sub.L (the distance between the aircraft's center of rotation 7 and the inertial navigation system 4) and the cross-track velocity is then related back to the initial east component of gyro bias error. The necessary parameter determinations may be made through calculations performed on the aircraft with the flight or navigation computer.
While the above-described system provides a useful technique for calibration of the navigation instruments, certain errors must be compensated to render that method or technique practical. Some of these result from the configuration of the aircraft while others reflect the condition of the runway surface and the surrounding physical environment. These factors complicate accurate measurement of the cross-track velocity and must be accounted for to prevent contamination of the various computations.
As discussed above, two of the three main sources of error may be readily compensated. The first of these, the crab angle error .beta., is a measure of the misalignment of the aircraft body with the ground track direction and reflects the fact that the wheels of an aircraft are not always pointed straight ahead while taxiing. This misalignment may result from the turning of the aircraft on the runaway, misalignment of the landing gear, unequal tire pressures and/or the wind's force transverse to the aircraft's tail. Each of these factors may cause some rotation of the aircraft relative to the tracking direction. The crab angle error is estimated by observing the cross-heading velocity V.sub.C during periods when the ground speed is large. The estimated crab angle is then used to make corrections to cross-track velocity for estimating the initial east component of gyro error during periods when ground speed and turning rate are small.
Another error implicit in the above method is produced by the lever arm R.sub.L that separates the center of rotation of the aircraft from the inertial navigational system (generally located forward of the main landing gear). This error produces an additional cross-heading velocity bias that contaminates the observed value. The lever arm is estimated by observing the cross-heading velocity during periods when the turning rate is large. The estimated lever arm is then used to make corrections for estimating initial east gyro error during periods when ground speed and turning rates are small.
A third important error source cannot be adequately modelled due to its essentially transient and random nature. That error, .delta.V.sub.n, is due to lateral and rotational motions of the aircraft while taxiing. Such velocity transients can result from bumps in the runway and their effects 8 upon the landing gear suspension system. This can cause the aircraft to roll and to translate both right and left as shown in FIG. 3, a frontal view of an aircraft for illustrating the relationship between landing gear suspension system motion and cross-heading velocity transients (.delta.V.sub.n) 10. Unfortunately, the resultant sharp velocity spikes, although transient, are so large relative to the cross-heading velocity that they can overwhelm the error due to the initial east direction gyro bias error.